CN104842564A - NSGA-II-based three-dimensional printing multi-task optimal scheduling method - Google Patents

Abstract

The invention provides an NSGA-II-based three-dimensional printing multi-task optimal scheduling method, mainly using a non-dominated sorting genetic algorithm with an elitist strategy to realize three-dimensional printing multi-task optimal scheduling. Under a gradually customized large-scale production mode for a three-dimensional printing product, overall interests of a three-dimensional printing service provider and customers with demands, and a time limit-cost-resource-quality four-dimensional multi-task optimal scheduling model is built. Print resolution price differences are included within the model range for the first time, and printing tasks transmitted in real time are subjected to optimal scheduling, so the optimization effects of being the shortest in service time, the lowest in production cost, the shortest in wait time and idle time and minimum in printing accuracy deviation in three-dimensional printing multi-task production are respectively achieved, and the NSGA-II-based three-dimensional printing multi-task optimal scheduling method has better practical value and broad application prospects in the field of three-dimensional printing manufacturing.

Description

A kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II

Technical field

The present invention is specifically related to a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II; belong to the scheduling problem in advanced manufacturing running systems; customize gradually at 3 D-printing product, under large-scale production pattern, the Optimized Operation utilizing the non-dominated sorted genetic algorithm of band elitism strategy to realize 3 D-printing multitask to produce.

Background technology

As a kind of emerging technology, three-dimensional printing technology is considered to one of principal element guiding the third time industrial revolution.And in the Hanoverian, Germany industrial fair in April, 2013, " fourth industrial revolution " (also known as industry 4.0, Industry 4.0) strategy is formally released, and obtain the extensive approval of scientific research institution and industrial circle all over the world.During in November, 2014, premier Li Keqiang accessed Germany, announce that two countries will carry out industry 4.0 cooperation.Industry 4.0 projects are mainly divided into intelligent plant, intelligence is produced and the large theme of Intelligent logistics three, wherein intelligence produce relate generally to whole enterprise production logistics management, human-computer interaction and the application etc. of 3D technology in industrial processes.In industrial 4.0 epoch, following manufacturing business model to solve Customer Problems, will walk soft manufacture+personalized customization road.Therefore, the large-scale customizationization production how realizing 3D printing will be the main direction of studying in following academic research field and the field of manufacturing.

Have a large amount of about production scheduling problems in existing document, multiple-objection optimization and genetic algorithm (GeneticAlgorithm, GA) research, if Haghighi A etc. is at " Uncertainty analysis of water supplynetworks using the fuzzy set theory and NSGA-II " (Engineering Applications ofArtificial Intelligence, 2014, NSGA-II algorithm is utilized to carry out hydraulic analysis to the feed pipe network with uncertain coefficient of pipe friction and node demand 32:270-282), and demonstrate the validity of NSGA-II in online fuzzy is analyzed, Ghodratnama A etc. are at " Solving a new multi-obiectivemulti-route flexible flow line problem by multi-objective particle swarm optimizationand NSGA-II " (Journal of Manufacturing Systems, 2014) establish minimal time delay, minimum process cost and minimal path alternative costs three Mathematical Modelings for multipath flexible production line in, and utilize NSGA-II and MOPSO method to be optimized model to solve, Bayat M etc. are at " Dynamicmulti-objective optimization of industrial radial-flow fixed-bed reactor of heavyparaffin dehydrogenation in LAB plant using NSGA-II method " (Journal of theTaiwan Institute of Chemical Engineers, 2014, 45 (4): 1474-1484) NSGA-II counterweight industrial paraffin dehydrogenation Radial folw fixed-bed reactor is utilized to carry out multiobjective Dynamic Optimization in, draw maximum paraffin output capacity, and make to select to maximize, Bandyopadhyay S etc. are at " Solving multi-objective parallelmachine scheduling problem by a modified NSGA-II " (Applied MathematicalModeling, 2013,37 (10): 6718-6729.) utilize the NSGA-II algorithm of original NSGA-II, SPEA2 and improvement to carry out multiple parallel machine scheduling research in respectively, and demonstrate the validity of algorithm, Rokh B etc. are at " Proposing an efficient combination of interesting measures for mining associationrules via NSGA-II " (Technology, Communication and Knowledge (ICTCK), 2014International Congress on.IEEE, utilize the correlation rule of NSGA-II algorithm research data sample 2014:1-7), and verify that the combination of confidence level and cosine square is more effective to rules selection, Dixit S etc. are at " Optimal location and sizing of SVC for minimization of power loss and voltagedeviation using NSGA II " (Communication Systems and Network Technologies (CSNT), 2014 Fourth International Conference on.IEEE, 2014:975-980) in utilize NSGA-II to calculate to make the optimum SVC site and size that energy loss is minimum and voltage deviation is minimum.

In addition, also some Patents occurs, as " a kind of satellite parallel test resource collocation method based on genetic algorithm " (patent No.: 201210046718.5,2012-02-27) of Zheng Zheng etc.; " a kind of cloud computing method for scheduling task based on improving NSGA-II " (patent No.: 201410220452.0,2014-05-22) of Xue Shengjun etc.; " a kind of scheduling graph optimization method based on multi-objective genetic algorithm " (patent No.: 201210142732.5,2012-05-10) of Lei Xiaohui etc.; " tire-mold processing and assembling integrated optimization method based on NSGA-II " (patent No.: 201410318457.7,2014-07-04) of Li Zhi etc.

Below are all genetic algorithm, production scheduling and multi-objective optimization question application study situations in recent years, but up to the present, not yet have the multi-task scheduling Study on Problems achievement relating to 3 D-printing to occur.3 D-printing also belongs to a kind of manufacture process, and its task scheduling process simply can classify as a kind of NP-hard (Non-deterministic Polynomial) problem.Dispatching technique for this kind of task must can adapt to change and the inefficacy of various assembly, various Mutagens such as order change, supplier's change, the Production design that can respond inside and outside in time change (Process Plans change) etc., and multiobject optimization can be met, comprise cost, quality, time and system flexibility etc.Multi-objective optimization question (Multi-obiective Optimization Problem, MOP) proposed in 1896 by Italian economist Vilfredo Pareto the earliest, this optimization problem often can not obtain only optimal solution, but obtains one group of Pareto optimal solution with the form of set.NSGA-II is that the people such as Deb proposed in 2000, also be one of classic Evolutionary Multiobjective Optimization up to now, quick non-dominated ranking method is carried out classification computing by NSGA-II, introduces crowding distance comparison operator and elite's retention strategy, maintains the diversity of population preferably.On the basis of NSGA, quick non-dominated ranking method is carried out classification computing by NSGA-II, reduces computation complexity; Replace fitness in NSGA and share method, introduce crowding distance comparison operator and the solution that grade same after non-dominated ranking has identical fitness value is distinguished, make the individuality being in current optimum front end expand to whole optimum front end and be uniformly distributed; Utilize elite's retention strategy, make compete by individual offspring and its parent selecting to enter procreation pond to produce population of future generation, try one's best, remain the excellent individuality of gene more, improve Evolution of Population level.

Summary of the invention

In order to overcome the shortcoming of prior art existence with not enough; the object of this invention is to provide a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II; utilize the non-dominated sorted genetic algorithm of band elitism strategy; according to 3 D-printing service provider and scale customized customer demand; multiple print out task uploaded in real time is dispatched to corresponding printing device according to the rational method of salary distribution, realizing service time that businessman and client be all satisfied with, prints cost, idle waiting time and printing precision deviation and minimize.

The technical solution adopted for the present invention to solve the technical problems is:

Based on a 3 D-printing multitask Optimization Scheduling of NSGA-II, comprise the steps:

1) the task printing type of selected 3 D-printing, task assign the mode of mode and printed material;

2) set up duration-the four-dimensional Multiobjective Optimal Operation model of cost-resource-quality, comprise optimization aim and the constraints of multi-task scheduling;

3) random generation initial population P ₀, non-dominated ranking is carried out to all individualities, then according to the corresponding fitness value of level allocation of individuality sequence, namely solves the target function value of described Multiobjective Optimal Operation model;

4) to the population P after sequence ₀carry out genetic manipulation, obtain new progeny population Q ₀;

5) by population P _twith its progeny population Q _tmerge, obtain new population R _t, t=0 when evolving initial; Population R after being combined _tcarry out non-dominated ranking, obtain optimum front end F _i(i=1,2 ...);

6) to whole F _isort according to crowding distance, choose optimum individuality according to championship strategy, form population P _t+1;

7) to population P _t+1carry out genetic manipulation, form sub-population Q _t+1, take evolutionary generation as end condition, if current evolutionary generation is less than the evolutionary generation of end condition, then return step 3), repeat; Otherwise, export final result.

Further, described step 4) genetic manipulation, represent individual by chromosomal mode, the positional representation print out task numbering at chromogene place, genic value is the printer numbering that print out task is assigned to, and chromosome adopts real coding mode; Simulation binary system interior extrapolation method and multinomial variation method is adopted to carry out genetic manipulation.

Describedly solve in the process of target function value, for representing the occupied situation of printer, printer attribute and trend of work storehouse are set, wherein, trend of work storehouse is controlled by event triggered fashion, and trigger conditions comprises that print out task is assigned to printer, print out task starts to print and current print out task completes; Print out task is assigned to locking printer when printer and print out task start to print, release printer when current print out task completes.

The production delay of existing 3D printed product may cause order delayed for delivery date, cannot normally shipment, completes in advance, the idle waiting time can be caused to increase, lose time, resource and cost, and produces more stock.In addition, printing precision deviation is crossed conference and is caused the problems such as CSAT declines, quantity on order declines, precision price difference and production cost raising.The present invention is directed to the comprehensive profit of 3D print service supplier and product demand client; establish duration-the four-dimensional Multiobjective Optimal Operation model of cost-resource-quality; first printing precision price difference is based upon in model scope; NSGA-II algorithm is utilized to solve 3 D-printing multitask Optimal Scheduling first; the non-dominated sorted genetic algorithm of band elitism strategy is utilized to carry out multiple-objection optimization to object function; produce for 3 D-printing scale customized and provide strong theoretical foundation, for industrial 4.0 epoch contribute to a strength.

In addition; the present invention customizes gradually at 3 D-printing product, under large-scale production pattern; scheduling is optimized for the print out task assigned in real time; solve that serviced shortest time, production cost that 3 D-printing multitask produces are minimum respectively, idle waiting shortest time and the minimum optimization problem of printing precision deviation, manufacture field at 3 D-printing and there is good practical value and wide application prospect.

Accompanying drawing explanation

Fig. 1 is that related tasks of the present invention is assigned, distributed printer, print procedure and task delivery process figure;

Fig. 2 is the algorithm flow chart of NSGA-II of the present invention;

Fig. 3 is the gene expression that NSGA-II of the present invention encodes.

Detailed description of the invention

The present invention utilizes NSGA-II Multipurpose Optimal Method to realize 3 D-printing multitask Optimized Operation, and implementation step is as follows:

1. 3 D-printing pattern is generally changed

After 3 D-printing multi-task scheduling refers to that 3 D-printing task is assigned, requiring that (printing precision, delivery time, printing cost, printed material etc.) are dispensed to corresponding idle print machine according to certain printing, is that a series of print out task is assigned, is dispensed to suitable printer, the process of printing.From the time, scheduling scheme can be divided into generate for 3 D-printing multi-task scheduling and scheduling scheme performs two stages.First stage refers to and generates an optimum or preferably scheduling scheme by the means such as optimization of planning strategies for, and the prerequisite that scheme is normally run refers to that printing environment (task matching and printer modes etc.) is changeless.The implementing precondition of second stage is that actual printing environment is consistent with assumed conditions, otherwise need suitably revise former scheduling scheme or adjust.

Usually, after 3 D-printing task is assigned, businessman will according to the related needs of print out task and Optimized Operation strategy by task matching to suitable printing device.Conveniently problem modeling, needs to carry out further abstract process to practical problem:

1) task printing type

3 D-printing mode can be divided into solidity printing, flexible print and mixing to print three kinds.Solidity prints the while of referring to single printer only can serve a print out task, generally, if single printer only has a shower nozzle, then can only choose this kind of printing type.Flexible print refers to single print out task to be split out multiple part and consign to different printers respectively and prints simultaneously.This kind of printing type can above reduce printing device largely because moving up and down the mechanical damage brought.Mixing printing refers to solidity printing and flexible print two kinds of modes are carried out simultaneously.For different task printing types, should choose different optimizing scheduling schemes, the present embodiment considers solidity printing type.

2) task assigns mode

3 D-printing task can be divided into static state to assign, dynamically assign and flexibility assigns three kinds.Static state is assigned and is referred to when formulating operation plan, and distribute assuming that all tasks have been assigned and waited and print, this kind of mode is the most simple mode of simulating actual conditions.Dynamically assign and refer to each print out task and assign successively in print procedure, the time of assigning can be determined also can be determined by consumer by businessman, actual conditions of more fitting.Flexibility assigns a certain special circumstances that the task of referring to is assigned, and namely businessman assigns in advance through the movable print out task that allows such as a series of publicity, discounting, sales promotion, in advance customization.Because dynamically assign mode closing to reality situation more, the present embodiment only considers this kind of situation.

3) printed material angle

3 D-printing material can be divided into fixing and not fix two kinds of situations.Generally, the printer of a certain type after production is completed can a kind of printed material of fixed allocation, and only can change in manufacturing process, adds this kind of material, is called fixing printed material in this case.In addition, do not fix printed material and refer to a certain printer and can use multiple printed material, midway is changed the material of other types or is installed two or more materials simultaneously and print.For simplified model, the present embodiment considers fixing printed material mode.

2. 3 D-printing scheduling model

1) variable-definition

S={1,2 ..., s} represents print out task set; B={1,2 ..., b} represents printer set; L (mm) represents that printing precision mark is poor; Ta _iexpression task i assigns the time; P _iexpression task i preference printer; E _ithe demand amount of weaving silk of expression task i; VB _jrepresent operating efficiency (the unit interval amount of weaving silk, the D of printer j _jrepresent the unit interval power consumption of printer j; c ₀(unit/(0.1mm)) represents single precision price difference; c ₁(unit/mm) representation unit length material cost; c ₂(unit/(kwh)) representation unit electric cost; Wait1 _irepresent that print out task i prints the front stand-by period; Wait2 _jrepresent the printer j printing interval stand-by period; SB _ifor decision variable, represent the printer that task i is assigned to; SO _ifor decision variable, represent the page order of task i; Tb _iexpression task i is assigned to the time of printer; Th _iexpression task i starts the time-write interval; Tf _iexpression task i prints the deadline; If task i is printed with order k on printer j, then dependant variables x _ijk=1, otherwise equal 0.Wherein, i ∈ S, j ∈ B, k ∈ SO.

It should be noted that, in the present invention, print out task is assigned order and is task by the order printed, and printer is with printing precision difference l (mm) for standard descending, and it is the moment (Tb of task matching to printer that task assigns the moment _i=Ta _i).

2) model sets up (optimization aim and constraints thereof)

A) based on the performance indications f of deadline ₁(duration)

Supposing that each print out task terminates to printing from printing, there is not interruption in centre.According to each print out task from the time of assigning to having printed, calculate the average serviced time of each print out task, and with the minimized average serviced time for optimization aim.

$f_1=\min \frac{1}{s}{\mathrm{\Σ}}_{i=1}^s({\mathrm{Tf}}_i-{\mathrm{Ta}}_i)---\left(1\right)$

B) based on the performance indications f of cost ₂(cost)

Except time index, the indicator of costs with processing cost (comprising raw material cost, the energy cost etc.) punishment cost relevant with printing precision (fail to arrange precision print time, compensate corresponding loss) be main, and print cost for performance indications with minimized average.

$f_2=\min \frac{1}{s}[c_0{\mathrm{\Σ}}_{i=1}^{s}l{E}_i({\mathrm{SB}}_i-P_i)+c_1{\mathrm{\Σ}}_{i=1}^s{E}_i+c_2{\mathrm{\Σ}}_{i=1}^s({\mathrm{Tf}}_i-{\mathrm{Th}}_i)D_{{\mathrm{SB}}_i}]---\left(2\right)$

In formula (2), first expression formula is printing precision price difference, be directly proportional to the print out task demand amount of weaving silk and low precision, consider that the first-selected preference printer of print out task prints, represent low precision distance with preference printer and the difference of the coding being actually allocated to printer; Second expression formula is printed material cost, is directly proportional to the demand amount of weaving silk; 3rd expression formula is electric cost, is directly proportional to print out task total time-write interval.

C) based on the performance indications f of the utilization of resources ₃(resource)

There are following two kinds in print procedure and wait for situation: printer wait task arrival and print out task wait for that printer is idle.For reducing the standby wait of resource and task waiting time, printing pre-set time and printing being collectively referred to as the stand-by period time delay, building following performance indications:

$f_3=\min ({\mathrm{\Σ}}_{i=1}^s{\mathrm{wait}1}_i+{\mathrm{\Σ}}_{j=1}^b{\mathrm{wait}2}_j)---\left(3\right)$

D) based on the performance indications f of CSAT ₄(quality)

If printing device is to dispatch from the factory just set printing precision, then may there are some deviations between the satisfaction of printed product in the machining accuracy of each print out task and client.Based on the average serviced time with based in the optimizing index of average production cost, if the printing precision of emphasis product simply may occur only concentrating using certain a part of printing device, the situation of other idlenesses of equipment.Therefore, for better dispatching each print out task and printing device, machine burden and crudy two aspect need be considered.

$f_4=\min \left({\mathrm{\Σ}}_{i=1}^s\right|P\left(i\right)-\mathrm{SB}\left(i\right)\left|\right)---\left(4\right)$

Formula (4) for task preference printer with distribute printer change the degree scale of measurement.In order to generation trueness error little as far as possible, the printing cost that precision price difference produces is reduced while meeting customer need, less trueness error just can better guarantee CSAT simultaneously, and the performance indications based on customer satisfaction degree that above formula represents are one of performance indications that must consider.

In addition, bound for objective function has:

${\mathrm{\Σ}}_{j\∈B}{\mathrm{\Σ}}_{k\∈\mathrm{SO}}{x}_{\mathrm{ijk}}=1,\∀i\∈S---\left(5\right)$

${\mathrm{\Σ}}_{i\∈S}{x}_{\mathrm{ijk}}\≤1,\∀j\∈B,\∀k\∈\mathrm{SO}---\left(6\right)$

${\mathrm{Ta}}_i\≤{\mathrm{Tb}}_i,\∀i\∈S---\left(7\right)$

${\mathrm{Tf}}_i-{\mathrm{Th}}_i=\frac{E_i}{{\mathrm{VB}}_{{\mathrm{SB}}_i}},\∀i\∈S---\left(8\right)$

Formula (5) ensure that each print out task has and for once by the chance printed;

Formula (6) represents that the task that a certain printer prints simultaneously is no more than one;

Formula (7) ensures that task could be serviced after arriving;

Formula (8) expression task was directly proportional to the demand amount of weaving silk by the time-write interval, was inversely proportional to printer printing effect.

Dependant variables is determined according to decision variable and heuritic approach:

Step 1: obtaining information, determines page order SO and printer SB.

Step 2: determine current print out task, i=1.

Step 3: treat print out task i, determines its printer SB be assigned to _i.

Step 4: wait to be printed.Judge printer SB _iwhether idle, if the free time, start to print, determine time started Th _iwith deadline Tf _i; Otherwise wait for the printer free time (following the unbroken rule in midway when task prints).

Step 5: if print out task i is last print out task in page order SO, then algorithm terminates; Otherwise i=i+1, goes to Step 3.

Solve object function to need enlightenment formula algorithm, be represent the occupied situation of printer, be provided with printer attribute and trend of work storehouse, dynamic base is controlled by event triggered fashion.Trigger condition comprises that print out task is assigned to printer, print out task starts to print and current print out task completes three kinds of situations.Print out task is assigned to locking printer when printer and print out task start to print, release printer when current print out task completes.

3. Optimized model solves

The operating procedure of NSGA-II is as follows:

1) random generation initial population P ₀, non-dominated ranking is carried out to wherein all individualities, then according to the corresponding fitness value of level allocation of individuality sequence.

2) to the population P after sequence ₀carry out genetic manipulation (intersection, variation etc.), obtain new progeny population Q ₀.

3) by population P _twith its filial generation Q _tmerge, obtain new population R _t, t=0 when evolving initial.Population R after being combined _tcarry out non-dominated ranking, obtain optimum front end F _i(i=1,2 ...).

4) to whole F _isort according to crowding distance, choose optimum individuality according to championship strategy, form population P _t+1.

5) to population P _t+1carry out genetic manipulation, form sub-population Q _t+1, repeat, until meet end condition.

Wherein, to a certain individual i, if n _ifor arranging the individual amount of individual i in population, S _ifor the individual collections of being arranged by individual i, its quick non-dominated ranking process is:

1) all n are found out _ithe individuality of=0, and stored in set F ₁.

2) to set F ₁in each individual j, investigate the individual collections S that it is arranged _j, and make S set _jin each individual k arrange number of individuals n _k=n _k-1.

3) if now n _k=n _k-1=0, then newly-built set H preserves individual k.

4) non-dominant individual collections F ₁be labeled as rank=1, flag F ₁the non-dominant sequence of middle individuality is i _rank.

5) above progressive operation is done to set H, mark rank and i _rank

6) judging whether that all individualities are all labeled, is terminate, otherwise repeats previous step.

Wherein, being calculated as follows of crowding distance: if I is the non-dominant collection in population, I [i] _mrepresent that in set I, i-th individuality is relative to the value of m object function, sort (I, m) refers to and carry out non-dominated ranking to individuality under object function m, and calculation procedure is as follows:

1) individual number l=|I| is separated in set of computations I=sort (I, m).

2) the crowding initial value arranging each individual i is 0, i.e. I [i] _d=0.

3) to each object function m, each individual crowding distance on I border, front end is set to infinity, i.e. I [1] _d=I [l] _d=∞.

4) i=2 to l-1, individual crowding distance $I{\left[i\right]}_d=I{\left[i\right]}_d+(I{[i+1]}_m-I{[i-1]}_m)/(f_m^{\max }-f_m^{\min }).$

Order Instance below by 3 D-printing illustrates embodiments of the present invention.According to three-dimensional printer basic data and actual print job data, the validity of evaluation model and algorithm.Choose the printer four of different model, different size, apply printed material of the same race and carry out emulation experiment.Experiment printed material is most widely used ABS plastic, and price is c ₁=1.25 × 10 ^-3unit/mm (with reference to market price).Wherein, printer model, configuration information refer to table 1.

Table 1 printer model and configuration

Unit commercial power price is with reference to Nanjing standard c in 2009 ₂=0.75 yuan/(kwh).Precision price difference is set as c ₀=1 yuan/(0.1mm).From zero, choose and assign 3 D-printing task 15 continuously, print out task related data: task assigns time, task preference printing device, mission requirements printed material amount, refers to table 2.

Table 2 print job data

By test of many times, determine that the 3 D-printing multi-task scheduling simulation parameters based on NSGA-II is set as: Population Size pop=80, genetic evolution algebraically generation=1000, crossover probability P _c=0.9, mutation probability P _m=0.1.Based on above data, specific embodiment of the invention step is as follows:

1. chromosome coding.Because the decision variable of Optimized model has SO and SB two groups, and in order to simplified model, definition task page order S set O is print out task and assigns sequenced collection, therefore only needs to encode to SB.Represent individual by chromosomal mode, the positional representation print out task numbering at chromogene place, genic value is the printer numbering that print out task is assigned to, and chromosome adopts real coding mode, as Fig. 3.

2. initialize population.Initial population adopts the mode of stochastic generation, and chromogene is randomly drawed in printer set B, but needs in the set B range of definition.

3. target function value calculates.Solve target function value and need utilize heuritic approach, first obtain dependant variables according to each decision variable, and bring formula (1) respectively into and solve to (4).

4.Pareto classification

1) rank grad=1 is made;

2) get a solution x* as a reference from G for appointing population pop (G), solution every other in itself and population is compared;

3) if X* arranges every other solution, then make its rank grad (x*)=grad, repeat this process, until all solutions are all selected as with reference to solution in population;

4) individuality that all ranks are grad is deleted;

5) do not determined then to make grad=grad+1 by the individuality of rank if also exist in population, gone to 2).

5. crowding distance calculates.Ask each target function value f _k(x), k ∈ 1,2,3,4}, and press the large young pathbreaker's individuality of functional value { x ₁, x ₂..., x _xarrange.After having arranged, definition corresponds to minf _kwith maxf _kindividual min and max between crowding distance be infinitely great, in addition i, j ≠ min, i, j ≠ max, crowding distance is:

d _i，j(f _k)＝|f _k(x _i)-f _k(x _j)| (9)

Crowding distance in population between any two individualities is:

$d_{i,j}={\mathrm{\Σ}}_{k=1}^5{d}_{i,j}\left(f_k\right)---\left(10\right)$

6. select.Now population scale is 2n.First all individualities are arranged from small to large according to the grad after Pareto classification; Then, there is the individuality of identical grad value according to crowding distance order arrangement from big to small; Finally, front n individuality is chosen according to putting in order above as population of future generation.

7. intersect.Adopt simulation binary system intersection (Simulated Binary Crossover, SBC) method, it is jumped out locally optimal solution help population, avoids the positive role in Premature Convergence to be confirmed.If x _{r, i, k}the parent being Stochastic choice is individual, x _{i, k}(i=1,2) represent a kth gene position of the offspring individual that parent individuality produces after SBC, and producing new individuality is:

$\left\{\begin{array}{c}{x}_{1,k}=\frac{1}{2}[(1-{\mathrm{\β}}_k)\·x_{r,1,k}+(1+{\mathrm{\β}}_k)\·x_{r,2,k}]\\ x_{2,k}=\frac{1}{2}[(1+{\mathrm{\β}}_k)\·x_{r,1,k}+(1-{\mathrm{\β}}_k)\·x_{r,2,k}]\end{array}\right.---\left(11\right)$

If u is the random number in (0,1), η _cdefine the new individual profile exponent produced, equal population scale, β _k>=0 can be produced by following formula:

${\mathrm{\&beta;}}_k=\left\{\begin{array}{cc}{\left(2u\right)}^{1/({\mathrm{\&eta;}}_c+1)},& u<0.5\\ {\left[2(1-u)\right]}^{1/({\mathrm{\&eta;}}_c+1)},& u\&GreaterEqual;0.5\end{array}\right.---\left(12\right)$

8. make a variation.Adopt multinomial variation method, when population at individual does not get a promotion through constant generations, multinomial variation is carried out to the new individuality produced. u is the random number in [0,1] interval, η _mbe the profile exponent that user chooses, the form of multinomial variation is:

$x_k^{\&prime;}=x_k+\mathrm{\&delta;}\&CenterDot;(u_k-x_{\min }^k)---\left(13\right)$

$\mathrm{\&delta;}=\left\{\begin{array}{ccc}{[2u+(1-2u){(1-{\mathrm{\&delta;}}_1)}^{{\mathrm{\&eta;}}_m+1}]}^{\frac{1}{{\mathrm{\&eta;}}_m+1}}-1,& \mathrm{if}& u\&le;0.5\\ 1-{[2(1-u)+2(u-0.5){(1-{\mathrm{\&delta;}}_2)}^{{\mathrm{\&eta;}}_m+1}]}^{\frac{1}{{\mathrm{\&eta;}}_m+1}},& \mathrm{if}& u>0.5\end{array}\right.---\left(14\right)$

9. end condition.Take evolutionary generation as end condition, if current evolutionary generation is less than setting value, then return 3; Otherwise, export final result.

Based on above operation, show that a series of non-domination solution set is as table 3.

Table 3 NSGA-II non-dominant disaggregation

For the validity of verification algorithm and model, NSGA-II non-domination solution and standard genetic algorithm single object optimization result are contrasted, show that its degree of optimization is as table 4.Wherein single object optimization solution is $f_1^{*}=31208.89,$ $f_2^{*}=1468.32,f_3^{*}=131816,f_4^{*}=0,$ The degree of optimization of each object function is by formula represent, wherein n=1,2,3.

Table 4 degree of optimization

Compared by the degree of optimization of table 4 and draw, scheme 1 and scheme 7 all can draw the solution being comparatively better than other schemes and single object optimization result, but the printing precision deviation of two schemes is respectively 8 and 4 as can be seen from Table 3, can decision scheme 7 be therefore NSGA-II scheduling preferred plan.

Claims (6)

1., based on a 3 D-printing multitask Optimization Scheduling of NSGA-II, it is characterized in that, comprise the steps:

1) the task printing type of selected 3 D-printing, task assign the mode of mode and printed material;

2) set up duration-the four-dimensional Multiobjective Optimal Operation model of cost-resource-quality, comprise optimization aim and the constraints of multi-task scheduling;

3) random generation initial population P ₀, non-dominated ranking is carried out to all individualities, then according to the corresponding fitness value of level allocation of individuality sequence, namely solves the target function value of described Multiobjective Optimal Operation model;

4) to the population P after sequence ₀carry out genetic manipulation, obtain new progeny population Q ₀;

5) by population P _twith its progeny population Q _tmerge, obtain new population R _t, t=0 when evolving initial; Population R after being combined _tcarry out non-dominated ranking, obtain optimum front end F _i(i=1,2 ...);

6) to whole F _isort according to crowding distance, choose optimum individuality according to championship strategy, form population P _t+1;

7) to population P _t+1carry out genetic manipulation, form sub-population Q _t+1, take evolutionary generation as end condition, if current evolutionary generation is less than the evolutionary generation of end condition, then return step 3), repeat; Otherwise, export final result.

2. a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II according to claim 1, it is characterized in that, described step 1) in, task printing type comprises solidity printing, flexible print and mixing and prints, solidity prints the while of referring to single printer only can serve a print out task, flexible print refers to single print out task to be split out multiple part and consign to different printers respectively and prints simultaneously, and mixing printing refers to solidity printing and flexible print two kinds of modes are carried out simultaneously; Described task is assigned mode and is comprised static state and assign, dynamically to assign and flexibility is assigned, and static state is assigned and referred to when formulating operation plan, distributes assuming that all tasks have been assigned and waited and prints; Dynamically assign and refer to each print out task and assign successively in print procedure; Flexibility assigns a certain special circumstances that the task of referring to is assigned; Described printed material comprises fixing a kind of printed material and uses multiple printed material.

3. a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II according to claim 1 and 2, is characterized in that, described step 2) in, optimization aim comprises as follows:

1. based on the performance indications of deadline, i.e. duration f ₁; Supposing that each print out task terminates to printing from printing, there is not interruption in centre;

$f_1=\min \frac{1}{s}\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}(T{f}_i-T{a}_i)---\left(1\right)$

In formula, Tf _iexpression task i prints the deadline; Ta _iexpression task i assigns the time; S={1,2 ..., s} represents print out task set;

2. based on the performance indications of cost, i.e. cost f ₂; Comprise the punishment cost that processing cost is relevant with printing precision, print cost for performance indications with minimized average;

$f_2=\min \frac{1}{s}[c_0\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{\mathrm{lE}}_i({\mathrm{SB}}_i-P_i)+c_1+\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{E}_i+c_2\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}(T{f}_i-{\mathrm{Th}}_i)D_{{\mathrm{SB}}_i}]---\left(2\right)$

In formula, l represents that printing precision mark is poor, mm; E _ithe demand amount of weaving silk of expression task j; c ₀represent single precision price difference, unit/(0.1mm); c ₁representation unit length material cost, unit/mm; c ₂representation unit electric cost, unit/(kwh); P _iexpression task i preference printer; SB _ifor decision variable, represent the printer that task i is assigned to; Th _iexpression task i starts the time-write interval; D _jrepresent the unit interval power consumption of printer j;

3. based on the performance indications of the utilization of resources, i.e. resource f ₃; Printer wait task arrival and print out task wait printer free time is there is in print procedure; For reducing the standby wait of resource and task waiting time, printing pre-set time and printing being collectively referred to as the stand-by period time delay, building following performance indications:

$f_3=\min (\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{\mathrm{wait}1}_i+\underset{j=1}{\overset{b}{\mathrm{\&Sigma;}}}{\mathrm{wait}2}_j)---\left(3\right)$

In formula, wait1 _irepresent that print out task i prints the front stand-by period; Wait2 _jrepresent the printer j printing interval stand-by period;

4. based on the performance indications of CSAT, i.e. quality f ₄; In order to generation trueness error little as far as possible, reduce the printing cost that precision price difference produces while meeting customer need, just less trueness error can better guarantee CSAT simultaneously, build following performance indications:

$f_4=\min \left(\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}\right|P\left(i\right)-\mathrm{SB}\left(i\right)\left|\right)---\left(4\right)$

Described constraints is as follows:

① ${\mathrm{\&Sigma;}}_{j\&Element;B}{\mathrm{\&Sigma;}}_{k\&Element;\mathrm{SO}}{x}_{\mathrm{ijk}}=1,\&ForAll;i\&Element;S,$ Ensure that each print out task has and for once by the chance printed,

In formula, B={1,2 ..., b} represents printer set; SO _ifor decision variable, represent the page order of task i; If task i is printed with order k on printer j, then dependant variables x _ijk=1, otherwise equal 0; Wherein, i ∈ S, j ∈ B, k ∈ SO;

② ${\mathrm{\&Sigma;}}_{i\&Element;S}{x}_{\mathrm{ijk}}\&le;1,\&ForAll;j\&Element;B,\&ForAll;k\&Element;\mathrm{SO},$ Represent that the task that a certain printer prints simultaneously is no more than one;

③ ${\mathrm{Ta}}_i\&le;{\mathrm{Tb}}_i,\&ForAll;i\&Element;S,$ Could be serviced after guarantee task arrives,

In formula, Tb _iexpression task i is assigned to the time of printer;

④ ${\mathrm{Tf}}_i-{\mathrm{Th}}_i=E_i/{\mathrm{VB}}_{{\mathrm{SB}}_i},\&ForAll;i\&Element;S,$ Expression task was directly proportional to the demand amount of weaving silk by the time-write interval, was inversely proportional to printer printing effect,

In formula, VB _jrepresent the operating efficiency of printer j, i.e. the unit interval amount of weaving silk.

4. a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II according to claim 1, it is characterized in that, described step 3) in the target function value that solves utilize heuritic approach, first obtain dependant variables according to decision variable, concrete steps are as follows:

1. obtaining information, determines page order SO and printer SB;

2. current print out task is determined, i=1;

3. treat print out task i, determine its printer SB be assigned to _i;

4. etc. to be printed: to judge printer SB _iwhether idle, if the free time, start to print, determine time started Th _iwith deadline Tf _i; Otherwise wait for that printer is idle, follow the unbroken rule in midway when task prints;

If 5. print out task i is last print out task in page order SO, then algorithm terminates; Otherwise 3. i=i+1, go to.

5. a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II according to claim 1, it is characterized in that: described step 4) genetic manipulation, represent individual by chromosomal mode, the positional representation print out task numbering at chromogene place, genic value is the printer numbering that print out task is assigned to, and chromosome adopts real coding mode; Simulation binary system interior extrapolation method and multinomial variation method is adopted to carry out genetic manipulation.

6. a kind of 3 D-printing multitask Optimization Scheduling based on NSGA-II according to claim 4, it is characterized in that, describedly solve in the process of target function value, for representing the occupied situation of printer, printer attribute and trend of work storehouse are set, wherein, trend of work storehouse is controlled by event triggered fashion, and trigger conditions comprises that print out task is assigned to printer, print out task starts to print and current print out task completes; Print out task is assigned to locking printer when printer and print out task start to print, release printer when current print out task completes.